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Cryptographic approach to quantum metrology

Nathan Shettell1, Elham Kashefi1,2, and Damian Markham1,3

  • 1Laboratoire d'Informatique de Paris 6, CNRS, Sorbonne Université, 4 place Jussieu, 75005 Paris, France
  • 2School of Informatics, University of Edinburgh, EH8 9AB Edinburgh, United Kingdom
  • 3Japanese-French Laboratory for Informatics, CNRS, National Institute for Informatics, University of Tokyo, Tokyo, Japan

Phys. Rev. A 105, L010401 – Published 4 January, 2022

DOI: https://doi.org/10.1103/PhysRevA.105.L010401

Abstract

We consider a cryptographically motivated framework for quantum metrology in the presence of a malicious adversary. We begin by devising an estimation strategy for a (potentially) altered resource (due to a malicious adversary) and quantify the amount of bias and the loss in precision as a function of the introduced uncertainty in the resource. By incorporating an appropriate cryptographic protocol, the uncertainty in the resource can be bounded with respect to the soundness of the cryptographic protocol. Thus the effectiveness of the quantum metrology problem can be directly related to the effectiveness of the cryptography protocol. As an example, we consider a quantum metrology problem in which resources are exchanged through an unsecured quantum channel. We then construct two protocols for this task which offer a trade-off between difficulty of implementation and efficiency.

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